President Barak Obama’s announcement of immigration changes that will protect nearly 5 million people living in the US illegally from deportation has infuriated Republicans, but has also left them scrambling for a response that won’t undermine their prospects in the 2016 presidential election.

Obama’s measure, which will make nearly half of those living the US illegally eligible for work permits, has been criticized by Republicans as an amnesty for lawbreakers and abuse of presidential powers.

In a news conference Friday, House Speaker John Boehner accused Obama “damaging the presidency itself” with his unilateral action on immigration and says the House will not stand idle and let it happen, but he offered no hint of what steps the House might take.

Fresh off their big midterm elections victory, where they took control of the Senate and retained control of the House, congressional Republicans thought they might be on the offensive against a chastened Obama.

Instead they are left trying to balance the demands of irate conservatives without alienating moderates, Hispanics and other voters.

In a televised address to the nation on Thursday evening, Obama defended his actions and challenged Republicans lawmakers to focus their energy not on blocking his measures but on approving long-stalled legislation to take their place.

“To those members of Congress who question my authority to make our immigration system work better, or question the wisdom of me acting where Congress has failed, I have one answer: Pass a bill,” Obama said, flexing his presidential powers just two weeks after his political standing was challenged in the midterm elections.

Despite Obama’s challenge to Republicans to pass a broader immigration bill, his actions and the angry Republican response could largely stamp out those prospects for the remainder of his presidency, ensuring that the contentious debate will carry on for some time.

The main question facing Republicans how to undo an action set to take effect without Congress doing anything, with no obvious legislative vehicle for doing so and Obama able to veto any legislative solution they derive.

Conservative lawmakers are pushing to insert language in upcoming must-pass spending bills to block Obama’s order. Party leaders warn that could lead to a government shutdown.

Numerous Republicans have discussed suing the president over his immigration orders, or expanding a lawsuit already planned over the health care law to include immigration. Yet they fret it would take too long and wouldn’t have the effect of blocking Obama’s orders from going into effect.

Others said that Republicans had an obligation to try to craft their own legislation. But chances of success seemed remote, at best.

While Obama’s measures are sweeping in scope, they still leave more than half of the 11 million people living in the US illegally in limbo. The president announced new deportation priorities that would compel law enforcement to focus its efforts on tracking down serious criminals and people who have recently crossed the border, while specifically placing a low priority on those who have been in the United States for more than 10 years.

The president spent months trying to gain a House vote on the Senate bill, frustrating immigration advocates and some Democrats who wanted him to instead take action on his own. While Obama had long insisted that his powers to halt deportations were limited, the White House began seriously exploring options for unilateral action.

Still, that process has been beset by delays, especially Obama’s decision to hold off on announcing the executive orders until after the midterms. Some Democrats had feared that thrusting the immigration debate to the forefront of the campaign would hurt their chances of keeping control of the Senate, though the White House’s delay ultimately did little to stem their defeats.